Multiply the expression as you would multiply polynomials. $$\left( x ^ { 11 / 2 } + y ^ { 15 / 2 } \right) ^ { 2 }$$
A) $\quad x ^ { 11 } + 2 x ^ { 11 / 2 } y ^ { 15 / 2 } + y ^ { 15 }$
B) $\quad x ^ { 11 } + x ^ { 11 } y ^ { 15 } + y ^ { 15 }$
C) $\quad x ^ { 11 } - 2 x ^ { 11 } y ^ { 15 } + y ^ { 15 }$
D) $\quad x ^ { 11 } + y ^ { 15 }$

Question

Quizplus · Accepted Answer

When we multiply the expression $(x^{11/2}+y^{15/2})^2$, we need to use FOIL (First, Outer, Inner, Last) method. This gives us:

$(x^{11/2}+y^{15/2})^2 = (x^{11/2}\cdot x^{11/2}) + (x^{11/2} \cdot y^{15/2}) + (y^{15/2} \cdot x^{11/2}) + (y^{15/2} \cdot y^{15/2})$

Simplifying this we get:

$x^{11} + 2x^{11/2}y^{15/2} + y^{15}$

Therefore, the best choice is $\boxed{	ext{(A)}\ x^{11}+2x^{11/2}y^{15/2}+y^{15}}$.

Multiply the Expression as You Would Multiply Polynomials (x11/2+y15/2)2\left( x ^ { 11 / 2 } + y ^ { 15 / 2 } \right) ^ { 2 }(x11/2+y15/2)2

Multiply the Expression as You Would Multiply Polynomials $\left( x ^ { 11 / 2 } + y ^ { 15 / 2 } \right) ^ { 2 }$